Discrete Unilateral Constrained Extended Kalman Filter in an Embedded System
Bibliographic record
Abstract
Since its publication in the 1960s, the Kalman Filter (KF) has been a powerful tool in optimal state estimation. However, the KF and most of its variants have mainly focused on the state estimation of smooth systems. In this work, we propose a new algorithm called the Discrete Unilateral Constrained Extended Kalman Filter (DUCEKF) that expands the capabilities of the Extended Kalman Filter (EKF) to a class of hybrid mechanical systems known as systems with unilateral constraints. Such systems are non-smooth in position and discontinuous in velocity. Lyapunov stability theory is invoked to establish sufficient conditions for the estimation error stability of the proposed algorithm. A comparison of the proposed algorithm with the EKF is conducted in simulation through a case study to demonstrate the superiority of the DUCEKF for the state estimation tasks in this class of systems. Simulations and an experiment were developed in this case study to validate the performance of the proposed algorithm. The experiment was conducted using electronic hardware that consists of an Embedded System (ES) called "Mikromedia for dsPIC33EP" and an external DAC-12 Click board, which includes a Digital-to-Analog Converter (DAC) from Texas Instruments.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".